Keep scrolling down for answers and more stats ...
1. He lives in a castle.
Hogwarts. Gandalf has no permanent residence.
Dumbledore
Gandalf
both
2. He dies in the books and/or movies.
Gandalf is then resurrected as Gandalf the White.
Dumbledore
Gandalf
both
3. He is played by Ian McKellen in the movies.
Dumbledore
Gandalf
both
4. He has a brother.
Aberforth Dumbledore.
Dumbledore
Gandalf
both
5. He entrusts a child and his friends with a top secret task in order to achieve the ultimate victory.
Harry Potter is a child for most of the books/movies. Neither Bilbo nor Frodo are children. As pointed out by @overtired in the comments, Pippin is not of (hobbit) adult age but he isn't entrusted with the task directly.
Dumbledore
Gandalf
both
6. His friends are birds and a horse.
The Great Eagles and Shadowfax. Dumbledore has a phoenix but has no horse friends (horse-like creatures, such as centaurs and hippogriffs are not horses).
Dumbledore
Gandalf
both
7. He is known for his spectacular fireworks.
Dumbledore
Gandalf
both
8. He does not live in England.
Gandalf lives in the Middle Earth, Dumbledore in Hogwarts, Scotland.
Dumbledore
Gandalf
both
9. A crucial part of defeating his nemesis lies in the destruction of a magical ring.
Morvolo Gaunt's Ring destroyed by Dumbledore is one of Voldemort's Horcruxes. In this way he also retrieved a Deathly Hallow - the stone. Gandalf needs to destroy the One Ring forged by Sauron.
Dumbledore
Gandalf
both
10. He is older.
Dumbledore is in his 100s, Gandalf is over 2000 years old (possibly over 24,000 years old)
Dumbledore
Gandalf
neither
11. He likes to smoke pipe-weed.
Dumbledore
Gandalf
both
12. His nemesis is known as "the Dark Lord".
Dumbledore
Gandalf
both
13. He is known for his sweet tooth.
Dumbledore
Gandalf
both
14. He speaks at least one fictional language (such as Dragon Language).
Dumbledore speaks Mermish (language of the merpeople from the lake) and Gobbledegook (the Goblin language). Gandalf speaks Hobbitish, Elvish and many more languages.